A low specific speed double suction pump vibration and noise reduction design method
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SHANGHAI KAIQUAN PUMP IND GROUP
- Filing Date
- 2026-05-12
- Publication Date
- 2026-06-12
Smart Images

Figure CN122197404A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a vibration reduction and noise reduction design method for a dual-suction pump, specifically a method for vibration reduction and noise reduction of a low specific speed dual-suction pump that analyzes pressure coefficient and sound pressure level, constructs an evaluation function for height h and distance d, and realizes parameter design and optimization of the structure at the impeller blade outlet. Background Technology
[0002] Double-suction pumps are characterized by high head and large flow rate, and are widely used in building fire protection, circulating water supply in engineering systems, cooling water circulation, boiler water supply, and industrial water supply and drainage. A double-suction pump mainly consists of a suction chamber, two back-to-back impellers, and a volute. Dynamic and static interference occurs between the impeller outlet and the volute, resulting in significant vibration and noise. To suppress vibration and noise, a structural design has been implemented for the impeller blades, which will significantly reduce vibration and noise. Summary of the Invention
[0003] To address the aforementioned problems, the main objective of this invention is to provide a vibration reduction and noise reduction design method for a low specific speed dual-suction pump, which involves analyzing pressure coefficient and sound pressure level, constructing an evaluation function for height h and distance d, and realizing parameter design and optimization of the structure at the impeller blade outlet.
[0004] The present invention solves the above-mentioned technical problems through the following technical solution: a vibration reduction and noise reduction design method for a low specific speed dual-suction pump, wherein a V-shaped structure is set at the blade outlet of the dual-suction pump impeller, and multiple V-shaped structures are arranged along the blade outlet axial direction; the vibration reduction and noise reduction design method for a low specific speed dual-suction pump includes the following steps: Step 1: Determine the pressure coefficient and sound pressure level based on numerical simulation; Step 2: Fit a two-dimensional function based on the pressure coefficient and sound pressure level data from Step 1; Step 3: Construct the evaluation function f(h, d) based on the two-dimensional function fitting conclusion in Step 2, and obtain the h and d corresponding to the optimal solution; where: d is the distance at the impeller blade outlet, and h is the height.
[0005] In a specific embodiment of the present invention, step 1 includes the following specific steps: Step 1.1: Based on the geometric parameters of the double-suction pump, establish a numerical simulation model of the double-suction pump; in this model, s monitoring points are set at different positions on the impeller and volute, namely T1, T2, T3, ..., T s-1 T s ; Step 1.2: Extraction of pressure coefficient from numerical simulation of dual-suction pump: Take the distance d from the impeller blade outlet i The height h is taken as h1, h2, h3, ..., h m-1h m Numerical simulation analysis of a double-suction pump was performed, and its pressure coefficient value was extracted. The pressure coefficient value is Q. j = (x i,1 x i,2 x i,3 ... x i,m-1 x i,m ); where i=1, 2, 3,…, n-1, n; j=i; x i,m When the distance is d i The height is h m The average pressure coefficient of s monitoring points over time; Step 1.3: Numerical simulation of sound pressure level extraction using a dual-suction pump; Take the distance d from the impeller blade outlet i The height h is taken as h1, h2, h3, ..., h m-1 h m Numerical simulation analysis of a dual-suction pump was performed, and its sound pressure level value was extracted. The sound pressure level value was W. j =(y i,1 y i,2 y i,3 ... y i,m-1 y i,m ); where i=1, 2, 3,…, n-1, n; j=i; y i,m When the distance is d i The height is h m The average pressure coefficient of s monitoring points.
[0006] In a specific embodiment of the present invention, step 2 includes the following specific steps: Step 2.1: Construct the set of pressure coefficient values from Step 1.2 and determine the function with respect to h and d. ; In the formula: A1, A2, A3, A4, A5, and A6 are constants; Step 2.2: Construct the set of sound pressure level values from Step 1.3 and determine the function of h and d. ; In the formula: B1, B2, B3, B4, B5, and B6 are constants.
[0007] In a specific embodiment of the present invention, step 3 includes the following specific steps: Step 3.1: Construct the evaluation function ; In the formula: Q is the average pressure coefficient, and W is the average sound pressure level; Step 3.2: Solve for the minimum value of the evaluation function f(h, d) to obtain the optimal values of height h and distance d; F(h,d) represents the constructed pressure coefficient value Q as a bivariate quadratic function of the distance d and height h at the impeller blade outlet.
[0008] T(h,d) represents the constructed sound pressure level W as a bivariate quadratic function of the distance d and height h at the impeller blade outlet.
[0009] The positive and progressive effects of this invention are as follows: The vibration reduction and noise reduction design method for low specific speed dual-suction pumps provided by this invention has the following advantages: In view of the lack of research on the vibration and noise of dual-suction pumps, the method analyzes the vibration and noise based on the pressure coefficient and sound pressure level, constructs an evaluation function for height h and distance d, and realizes the parameter design and optimization of the structure at the impeller blade outlet. Attached Figure Description
[0010] Figure 1-1 This is a schematic diagram of the external structure of the double-suction centrifugal pump of the present invention.
[0011] Figure 1-2 This is a schematic diagram of the monitoring point of the double-suction centrifugal pump of the present invention.
[0012] Figure 2 This is an overall schematic diagram of the impeller blades of the present invention.
[0013] Figure 3 This is a schematic diagram of the impeller blade of the present invention.
[0014] Figure 4-1 Time-domain plot of the original model.
[0015] Figure 4-2 Time-domain plot of biomimetic model 1.
[0016] Figure 4-3 Time-domain plot of biomimetic model 2.
[0017] Figure 4-4 Time-domain plot of biomimetic model 3.
[0018] Figure 4-5 Time-domain plot of biomimetic model 4.
[0019] Figure 4-6 Time-domain plot of biomimetic model 5.
[0020] Figure 4-7 Time-domain plot of biomimetic model 6.
[0021] Figure 4-8 Time-domain plot of biomimetic model 7.
[0022] Figure 4-9 Time-domain plot of biomimetic model 8.
[0023] Figure 4-10 Time-domain plot of biomimetic model 9.
[0024] Figure 5-1 Frequency domain diagram of the original model.
[0025] Figure 5-2 Frequency domain diagram of biomimetic model 1.
[0026] Figure 5-3 Frequency domain diagram of biomimetic model 2.
[0027] Figure 5-4 Frequency domain diagram of biomimetic model 3.
[0028] Figure 5-5 Frequency domain diagram of the biomimetic model 4.
[0029] Figure 5-6 Frequency domain diagram of biomimetic model 5.
[0030] Figure 5-7 Frequency domain diagram of biomimetic model 6.
[0031] Figure 5-8 Frequency domain diagram of biomimetic model 7.
[0032] Figure 5-9 Frequency domain diagram of the biomimetic model.
[0033] Figure 5-10 Frequency domain diagram of biomimetic model 9.
[0034] Figure 6-1 Original model sound pressure level diagram.
[0035] Figure 6-2 Sound pressure level diagram of biomimetic model 1.
[0036] Figure 6-3 Sound pressure level diagram of biomimetic model 2.
[0037] Figure 6-4 Sound pressure level diagram of biomimetic model 3.
[0038] Figure 6-5 Sound pressure level diagram of biomimetic model 4.
[0039] Figure 6-6 Sound pressure level diagram of biomimetic model 5.
[0040] Figure 6-7 Sound pressure level diagram of biomimetic model 6.
[0041] Figure 6-8 Sound pressure level diagram of biomimetic model 7.
[0042] Figure 6-9 Sound pressure level diagram of biomimetic model 8.
[0043] Figure 6-10 Sound pressure level diagram of biomimetic model 9. Detailed Implementation
[0044] The preferred embodiments of the present invention are given below with reference to the accompanying drawings to illustrate the technical solution of the present invention in detail.
[0045] Figure 1-1 This is a schematic diagram of the external structure of the double-suction centrifugal pump of the present invention. Figure 1-2 This is a schematic diagram of the monitoring point of the double-suction centrifugal pump of the present invention. Figure 2 This is an overall schematic diagram of the impeller blades of the present invention. Figure 3 The diagram above shows the structure of the impeller blades of this invention. The invention proposes a vibration and noise reduction design method for a low specific speed dual-suction pump, which involves setting a V-shaped structure at the blade outlet of the dual-suction pump impeller, with multiple V-shaped structures arranged along the blade outlet axial direction. This vibration and noise reduction design method for a low specific speed dual-suction pump includes the following steps: Step 1: Determine the pressure coefficient and sound pressure level based on numerical simulation; Step 2: Fit a two-dimensional function based on the pressure coefficient and sound pressure level data from Step 1; Step 3: Construct the evaluation function f(h, d) based on the two-dimensional function fitting conclusion in Step 2, and obtain the h and d corresponding to the optimal solution; where: d is the distance at the impeller blade outlet, and h is the height.
[0046] Step 1 includes the following specific steps: Step 1.1: Based on the geometric parameters of the double-suction pump, establish a numerical simulation model of the double-suction pump; in this model, s monitoring points are set at different positions on the impeller and volute, namely T1, T2, T3, ..., T s-1 T s ; Step 1.2: Extraction of pressure coefficient from numerical simulation of dual-suction pump: Take the distance d from the impeller blade outlet i The height h is taken as h1, h2, h3, ..., h m-1 h m Numerical simulation analysis of a double-suction pump was performed, and its pressure coefficient value was extracted. The pressure coefficient value is Q. j = (x i,1 x i,2 x i,3 ... x i,m-1 x i,m ); where i=1, 2, 3,…, n-1, n; j=i; x i,m When the distance is d i The height is h m The average pressure coefficient of s monitoring points over time; Step 1.3: Numerical simulation of sound pressure level extraction using a dual-suction pump; Take the distance d from the impeller blade outleti The height h is taken as h1, h2, h3, ..., h m-1 h m Numerical simulation analysis of a dual-suction pump was performed, and its sound pressure level value was extracted. The sound pressure level value was W. j =(y i,1 y i,2 y i,3 ... y i,m-1 y i,m ); where i=1, 2, 3,…, n-1, n; j=i; y i,m When the distance is d i The height is h m The average pressure coefficient of s monitoring points.
[0047] Step 2 includes the following specific steps: Step 2.1: Construct the set of pressure coefficient values from Step 1.2 and determine the function with respect to h and d. ; In the formula: A1, A2, A3, A4, A5, and A6 are constants; Step 2.2: Construct the set of sound pressure level values from Step 1.3 and determine the function of h and d. ; In the formula: B1, B2, B3, B4, B5, and B6 are constants.
[0048] Step 3 includes the following specific steps: Step 3.1: Construct the evaluation function ; In the formula: Q is the average pressure coefficient, and W is the average sound pressure level; Step 3.2: Solve for the minimum value of the evaluation function f(h, d) to obtain the optimal values of height h and distance d; F(h,d) represents the constructed pressure coefficient value Q as a bivariate quadratic function of the distance d and height h at the impeller blade outlet.
[0049] T(h,d) represents the constructed sound pressure level W as a bivariate quadratic function of the distance d and height h at the impeller blade outlet.
[0050] Below are some specific examples: Step 1: Determine the pressure coefficient and sound pressure level based on numerical simulation.
[0051] Step 1.1: Establish a numerical simulation model of the double-suction pump based on its geometric parameters. In this model, five monitoring points are set at different locations on the impeller and volute: T1, T2, T3, T4, and T5.
[0052] Step 1.2: Extraction of pressure coefficient from dual-suction pump numerical simulation.
[0053] 1) Take the distance d at the impeller blade outlet as 5mm, and the height h as 0.5mm, 0.84mm, and 1.34mm respectively, and perform numerical simulation analysis of the double suction pump, and extract the pressure coefficient value corresponding to its blade frequency. The pressure coefficient value is Q1 = (0.03748, 0.03312, 0.03672).
[0054] Where 0.03748 is the average value of the pressure coefficient corresponding to the blade frequency at the 5 monitoring points when the distance is 5 mm and the height is 0.5 mm; Where 0.03312 is the average pressure coefficient value corresponding to the blade frequency at the 5 monitoring points when the distance is 5mm and the height is 0.84mm; Where 0.03672 is the average value of the pressure coefficient corresponding to the blade frequency at the 5 monitoring points when the distance is 5 mm and the height is 1.34 mm.
[0055] 2) Take the distance d at the impeller blade outlet as 10mm, and the height h as 1.75mm, 2.1mm, and 2.68mm respectively, and perform numerical simulation analysis of the double suction pump, and extract the pressure coefficient value corresponding to its blade frequency. The pressure coefficient value is Q2 = (0.01991, 0.01910, 0.02462).
[0056] Where 0.01991 is the average value of the pressure coefficient corresponding to the blade frequency at the 5 monitoring points when the distance is 10mm and the height is 1.75mm; Where 0.01910 is the average value of the pressure coefficient corresponding to the blade frequency at the 5 monitoring points when the distance is 10mm and the height is 2.1mm; Where 0.02462 is the average pressure coefficient value corresponding to the blade frequency at the 5 monitoring points when the distance is 10mm and the height is 2.68mm.
[0057] 3) Take the distance d at the impeller blade outlet as 20mm, and the height h as 3.51mm, 4.2mm, and 6.42mm respectively, and perform numerical simulation analysis of the double suction pump, and extract the pressure coefficient value corresponding to its blade frequency. The pressure coefficient value is Q3 = (0.01720, 0.02129, 0.03794).
[0058] Where 0.01720 is the average pressure coefficient value corresponding to the blade frequency at the 5 monitoring points when the distance is 20mm and the height is 3.51mm; Where 0.02129 is the average value of the pressure coefficient corresponding to the blade frequency at the 5 monitoring points when the distance is 20mm and the height is 4.2mm; Where 0.03794 is the average pressure coefficient value corresponding to the blade frequency at the 5 monitoring points when the distance is 20mm and the height is 6.42mm.
[0059] Step 1.3: Numerical simulation of sound pressure level extraction using a dual-suction pump.
[0060] 1) Take the distance d at the impeller blade outlet as 5mm, and the height h as 0.5mm, 0.84mm, and 1.34mm respectively, and perform numerical simulation analysis of the double suction pump, and extract the sound pressure level value corresponding to its blade frequency. The sound pressure level value is W1 = (148.32, 147.93, 147.98).
[0061] The value of 148.32 dB is the average of the sound pressure level values corresponding to the leaf frequency at the five monitoring points when the distance is 5 mm and the height is 0.5 mm. The value of 147.93 dB is the average of the sound pressure level values corresponding to the leaf frequency at the five monitoring points when the distance is 5 mm and the height is 0.84 mm. The value of 147.98 dB represents the average sound pressure level at the leaf frequency of the five monitoring points when the distance is 5 mm and the height is 1.34 mm.
[0062] 2) The distance d at the impeller blade outlet is taken as 10 mm, and the height h is taken as 1.75 mm, 2.1 mm and 2.68 mm respectively. The numerical simulation analysis of the double suction pump is carried out, and the sound pressure level value corresponding to the blade frequency is extracted. The sound pressure level value is W2 = (145.92, 145.82 and 146.83).
[0063] The value of 145.92 dB is the average of the sound pressure level values corresponding to the leaf frequency at the five monitoring points when the distance is 10 mm and the height is 1.75 mm. The value of 145.82 dB is the average of the sound pressure level values corresponding to the leaf frequency at the five monitoring points when the distance is 10 mm and the height is 2.1 mm. The value of 146.83 dB represents the average sound pressure level at the leaf frequency of the five monitoring points when the distance is 10 mm and the height is 2.68 mm.
[0064] 3) Take the distance d at the impeller blade outlet as 20mm, and the height h as 3.51mm, 4.2mm, and 6.42mm respectively, and perform numerical simulation analysis of the double suction pump, and extract the sound pressure level value corresponding to its blade frequency. The sound pressure level value is W3 = (145.02, 145.15, 147.58).
[0065] The value of 145.02 dB is the average of the sound pressure level values corresponding to the leaf frequency at the five monitoring points when the distance is 20 mm and the height is 3.51 mm. The value of 145.15 dB is the average sound pressure level at the leaf frequency of the five monitoring points when the distance is 20 mm and the height is 4.2 mm. The value of 147.58 dB represents the average sound pressure level at the leaf frequency of the five monitoring points when the distance is 20 mm and the height is 6.42 mm.
[0066] Step 2: Two-dimensional function fitting of pressure coefficient and sound pressure level data.
[0067] Step 2.1: Construct the set of pressure coefficient values from Step 1.2 and determine the function with respect to h and d. .
[0068] Step 2.2: Construct the set of sound pressure level values from Step 1.3 and determine the function of h and d. .
[0069] Step 3: Construct the evaluation function f(h,d) and obtain h and d corresponding to the optimal solution.
[0070] Step 3.1: Construct the evaluation function .
[0071] Step 3.2: Solve for the minimum value of the evaluation function f(h,d) to obtain the optimal values of distance d and height h.
[0072] Based on the improved Newton-type iterative optimization method applicable to two-dimensional functions, the distance d and height h corresponding to the minimum value of the evaluation function are solved. The solution process is as follows: 1) Given d0=20, h0=3.51, and an initial point. The convergence accuracy ε is achieved as n→0.
[0073] 2) Calculation , , and .
[0074] 3) Find .
[0075] 4) Check the convergence accuracy. If ||X n+1 - X n If ||<ε, then If the calculation stops, proceed to n←n+1 and return to step 2) to continue the search.
[0076] 5) Obtain the distance d and height h. After multiple iterations, when the function reaches its minimum value... When = 1.38, the local minimum point is... = (16.53 1.13), then the distance d and height h are taken as 16.53 mm and 1.13 mm respectively.
[0077] Where d0 is the initial distance to the blade exit, h0 is the initial height to the blade exit, and X... 0 Let the initial point be composed of initial values d0 and h0. To evaluate the function f(h,d), for At approximate point X n gradient at, for In X n The Hessian matrix at the point, yes The inverse matrix, d k It is the direction of the (k+1)th search or iteration, X n+1 X n All are the next approximate points of the initial point, X * This is the minimum point.
[0078] Figure 4-1 The time-domain plot of the original model, Figure 4-2 Time-domain plot of biomimetic model 1 Figure 4-3 Time-domain plot of biomimetic model 2 Figure 4-4 Time-domain plot of biomimetic model 3 Figure 4-5 Bionic Model 4 Time Domain Plot Figure 4-6 Time-domain plot of biomimetic model 5 Figure 4-7 Time-domain plot of biomimetic model 6 Figure 4-8 Time-domain plot of biomimetic model 7 Figure 4-9 Time-domain plot of biomimetic model 8 Figure 4-10 Time-domain plot of biomimetic model 9 Figures 4-1 to 4-10 This is a time-domain diagram of 5 monitoring points for 10 impeller schemes of this invention, from... Figures 4-1 to 4-10 It can be seen that the pressure coefficient of the original model varies considerably, ranging from -0.2 to 0.15. In contrast, the pressure coefficients of the nine biomimetic models show significantly lower values than the original model, indicating that the biomimetic models have a noticeable effect on reducing the pressure coefficient. Among them, biomimetic model 4 exhibits the most significant effect in reducing the pressure coefficient, with its pressure coefficient ranging from -0.05 to 0.05.
[0079] Figure 5-1 Original model frequency domain plot, Figure 5-2 Frequency domain diagram of biomimetic model 1 Figure 5-3 Frequency domain diagram of biomimetic model 2 Figure 5-4 Bionic model 3 frequency domain diagram, Figure 5-5 Bionic model 4 frequency domain diagram, Figure 5-6 Bionic model 5 frequency domain diagram, Figure 5-7 Frequency domain diagram of biomimetic model 6 Figure 5-8 Frequency domain diagram of biomimetic model 7 Figure 5-9 Bionic model 8 frequency domain diagram, Figure 5-10 Frequency domain diagram of biomimetic model 9 Figures 5-1 to 5-10 This is a frequency domain diagram of 5 monitoring points for 10 impeller designs according to the present invention. From... Figures 5-1 to 5-10 It can be seen that the amplitude of monitoring point T1 is the largest and the amplitude of monitoring point T5 is the smallest. Therefore, reducing the amplitude of monitoring point T1 can significantly improve the vibration noise.
[0080] Figure 6-1 Original model sound pressure level diagram, Figure 6-2 Sound pressure level diagram of biomimetic model 1 Figure 6-3 Sound pressure level diagram of biomimetic model 2 Figure 6-4 Bionic Model 3 sound pressure level diagram, Figure 6-5 Sound pressure level diagram of biomimetic model 4 Figure 6-6 Sound pressure level diagram of biomimetic model 5 Figure 6-7 Sound pressure level diagram of biomimetic model 6 Figure 6-8 Sound pressure level diagram of biomimetic model 7 Figure 6-9 Bionic model 8 sound pressure level diagram, Figure 6-10 Sound pressure level diagram of biomimetic model 9 Figures 6-1 to 6-10 This is a sound pressure level diagram at 5 monitoring points for 10 impeller designs according to the present invention. From... Figures 6-1 to 6-10 It can be seen that T1 and T2 have relatively high sound pressure levels, while T5 has a relatively low sound pressure level. The sound pressure levels of the nine biomimetic models are significantly lower than those of the original model, with biomimetic model 8 having the lowest sound pressure level.
[0081] This invention analyzes pressure coefficient and sound pressure level to construct an evaluation function for height h and distance d, thereby realizing the parameter design and optimization of the structure at the impeller blade outlet.
[0082] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as defined by the appended claims and their equivalents.
Claims
1. A vibration reduction and noise reduction design method based on a low specific speed dual-suction pump, characterized in that: A V-shaped structure is provided at the blade outlet of the double-suction pump impeller, and multiple V-shaped structures are arranged along the blade outlet axial direction. The vibration reduction and noise reduction design method based on a low specific speed dual-suction pump includes the following steps: Step 1: Determine the pressure coefficient and sound pressure level based on numerical simulation; Step 2: Fit a two-dimensional function based on the pressure coefficient and sound pressure level data from Step 1; Step 3: Construct the evaluation function f(h, d) based on the two-dimensional function fitting conclusion in Step 2, and obtain the h and d corresponding to the optimal solution; where: d is the distance at the impeller blade outlet, and h is the height.
2. The vibration reduction and noise reduction design method based on a low specific speed dual-suction pump according to claim 1, characterized in that: Step 1 includes the following specific steps: Step 1.1: Based on the geometric parameters of the double-suction pump, establish a numerical simulation model of the double-suction pump; in this model, s monitoring points are set at different positions on the impeller and volute, namely T1, T2, T3, ..., T s-1 T s ; Step 1.2: Extraction of pressure coefficient from numerical simulation of dual-suction pump: Take the distance d from the impeller blade outlet i The height h is taken as h1, h2, h3, ..., h m-1 h m Numerical simulation analysis of a double-suction pump was performed, and its pressure coefficient value was extracted. The pressure coefficient value is Q. j = (x i,1 x i,2 x i,3 ... x i,m-1 x i,m ); in i=1, 2, 3,…, n-1, n; j=i; x i,m When the distance is d i The height is h m The average pressure coefficient of s monitoring points over time; Step 1.3: Numerical simulation of sound pressure level extraction using a dual-suction pump; Take the distance d from the impeller blade outlet i The height h is taken as h1, h2, h3, ..., h m-1 h m Numerical simulation analysis of a dual-suction pump was performed, and its sound pressure level value was extracted. The sound pressure level value was W. j =(y i,1 y i,2 y i,3 ... y i,m-1 y i,m ); where i=1, 2, 3,…, n-1, n; j=i; y i,m When the distance is d i The height is h m The average pressure coefficient of s monitoring points.
3. The vibration reduction and noise reduction design method based on a low specific speed dual-suction pump according to claim 1, characterized in that: Step 2 includes the following specific steps: Step 2.1: Construct the set of pressure coefficient values from Step 1.2 and determine the function with respect to h and d. ; In the formula: A1, A2, A3, A4, A5, and A6 are constants; Step 2.2: Construct the set of sound pressure level values from Step 1.3 and determine the function of h and d. ; In the formula: B1, B2, B3, B4, B5, and B6 are constants.
4. The vibration reduction and noise reduction design method based on a low specific speed dual-suction pump according to claim 1, characterized in that: Step 3 includes the following specific steps: Step 3.1: Construct the evaluation function ; In the formula: Q is the average pressure coefficient, and W is the average sound pressure level; Step 3.2: Solve for the minimum value of the evaluation function f(h, d) to obtain the optimal values of height h and distance d; F(h,d) represents the constructed pressure coefficient value Q as a bivariate quadratic function of the distance d and height h at the impeller blade outlet; T(h,d) represents the constructed sound pressure level W as a bivariate quadratic function of the distance d and height h at the impeller blade outlet.